Ion-driven permeation and surface recombination coefficient of deuterium for ion

of Nuclear Materials 202 (1993) 228-238 North-Holland

Journal

Ion-driven permeation of deuterium for ion

and surface recombination

coefficient

Takanori Nagasaki, Masahiro Saidoh, Reiji Yamada and Hideo Ohno Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki-ken 319-11, Japan

Received 16 October 1992; accepted 28 January 1993

The steady-state flux of deuterium permeation through an iron membrane (99.99 + % purity, 0.14 mm thickness) driven by a deuterium ion beam (5 keV D;, 1.0X 1015 D-atoms cm-’ s-l) was measured in the range of 30-1050°C. The permeation flux increased with increasing temperature above 200°C whereas it was roughly constant below 150°C. Such temperature dependence was observed for nickel and copper as well, and has been ascribed to the transition in the rate-limiting processes of the deuterium transport in the membrane. The recombination coefficient of deuterium on iron surface was evaluated from the permeation flux density. In the case of a-iron, the evaluated value agreed with a semitheoretical one estimated using literature data of adsorption probability and solubility. This agreement indicates that the release kinetics reflects the activation barrier for hydrogen (deuterium) adsorption.

1. Introduction In recent years hydrogen permeation through a metal membrane driven by an ionic or atomic hydrogen beam or hydrogen plasma has been extensively studied. It is because the phenomenon is closely related to the interaction of hydrogen with metal components in plasma devices. In addition, such experiments seem to be helpful to understand basic aspects of hydrogen release from metals. As reported in a previous paper [l], we have investigated ion-beam-driven permeation of deuterium through a nickel membrane. We measured the temperature dependence of the permeation flux and found that it exhibited a transition with temperature; the permeation flux increased with temperature above 400°C while it was roughly constant below 300°C. The dependence of the permeation flux on other parameters - implantation flux, implantation energy, and co existing gas-driven permeation flux - also changed around 300-400°C. On the other hand, we formulated the ion-driven permeation in the presence of the gasdriven permeation using a simple model, and classified the hydrogen transport in the membrane in terms of the rate-limiting processes (see section 2.1 and the appendix). Comparing the experimental results with the derived equations, we concluded that the observed 0022.3115/93/$06.00

0 1993 - Elsevier

Science

Publishers

transition with temperature was due to the transition in the rate-limiting processes. Above 4Oo”C, the transport was limited by the recombinative desorption in the injection side - the region shallower than the projected range of deuterium ions - and by the bulk diffusion in the back side (the RD regime). Below 3OO”C, in contrast, the transport was limited by the bulk diffusion both in the injection and the back sides (the DD regime). We subsequently measured the permeation flux for copper [2,3]. We observed that the dependence of the permeation flux both on the temperature and on the implantation flux changed around 200-300C similarly to that of nickel. Furthermore, we observed similar temperature dependence of the permeation flux for silver as well [4]. (The transition temperature was 300400°C.) We thus believe that the transition in the rate-limiting processes described above is common with all of the above three metals. Then does iron behave similarly? To answer this question is a purpose of the present experiment. In the RD regime, we can evaluate the recombination coefficient of deuterium at the injection surface from the permeation flux density (see section 2.1). We can also estimate the recombination coefficient semitheoretically using the adsorption probability and the solubility (see section 2.2). In fact, the recombina-

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T. Nagasaki et al. / Permeation and surface recombination coefficient of D for Fe

tion coefficients evaluated with the permeation flux density for nickel and copper agreed quantitatively with the semitheoretical estimates calculated with literature data of the adsorption probability and the solubility [3,5]. To further examine the relation for iron is another purpose of the present experiment.

2. Theoretical treatment 2.1. Description of the ion-driven permeation presence of gas-driven permeation

in the

Fig. 1 illustrates the steady-state hydrogen transport in a metal membrane exposed to a hydrogen ion beam as well as hydrogen gas. Here x is the distance from the injection surface, R, the mean projected range, and x0 the thickness of the membrane. C,(X) is the hydrogen concentration at x in the presence of the gas alone, and C,(x) is the increment in the hydrogen concentration due to the hydrogen implantation. Some of the hydrogen molecules impinging on the injection surface are dissociatively adsorbed on the surface, and then some of them diffuse toward the opposite (back) surface to be recombinatively desorbed from there, whereas the rest are recombinatively desorbed from the injection surface again. Similarly, the hydrogen implanted at R, then diffuses toward the injection or the back surface, and finally is recombinatively desorbed form there. The recycling flux and the permeation flux are none other than the hydrogen fluxes of

l”j*CtW”

side

Back Side

adsorption DRusion

*

Recombinative desorption (Recycling)

*

Recombinatlve dW3pW” (Permeation)

+

the recombinative desorption from the injection surface and from the back surface, respectively. In ref. [l], we classified the hydrogen transport in the metal membrane by the concentration profile. For the simultaneous gas- and ion-driven transport, we defined four transport regimes: the RR regime (C,(O) i C,(R,) i C,(x,J), the DR regime (C,(O) @ CJR,) + CP(x,)), the RD regime (C,(O) i C,(R,) B C,(x,)), and the DD regime (C,(O) K C,(R,) B C,(x,>). In the RD regime, for example, the hydrogen transport is limited by the recombinative desorption in the injection side and by the bulk diffusion in the back side. In each transport regime, the increment in the permeation flux density due to the implantation (Jr) can be approximated by a simple equation. For the gas-driven transport, on the other hand, we defined two transport regimes: the S regime (C,(O) + C,(x,)) and the D regime (Co(O) Z+ C,(x,J). In ref. [l], we explained the relation of the profile of Co(x) with the rate-limiting process as follows. When C,(O) i &.(~a), the transport (permeation) is limited by the dissociative adsorption on the injection surface or the recombinative desorption from the back surface. When C,(O) z+ Co(x,,), the transport (permeation) is limited by the bulk diffusion. We have found, however, that this interpretation is incorrect; even if C,(O) B C&(x,), the dissociative adsorption can be so slow as to limit the permeation flux. In other words, the correspondence is not unique between the concentration profile and the process which limits the magnitude of the permeation. In reality, the concentration profile corresponds to the process which limits the transport of the adsorbed hydrogen in the framework of our model (see section 2.2). The profile C,(O) + Co(x,) means that the transport of the adsorbed hydrogen is limited by the recombinative desorption at the back surface. We rename this transport regime the R regime. The profile Co(O) > C,(x,), in contrast, means that the transport of the adsorbed hydrogen is limited by the bulk diffusion. We call this transport regime the D regime. Although the interpretation of the profile of C,(x) in ref. [l] is thus incorrect, the expressions for Jr derived there are valid if we simply change the definition of the transport regime. (See ref. [6] for detailed discussion relating to the transport regime.) They are reprinted in the following for the convenience of later discussion. In the RR regime, K2 J,

Fig. 1. Schematic drawing of steady-state fluxes and concentration of hydrogen in a metal membrane exposed to a hydrogen ion beam and hydrogen gas.

229

+

-4

K,+K,

”

where +,, is the implantation

(1) flux density, and K, and

230

T. Nagasakiet al. / Permeationand surface recombinationcoefficientof D for Fe

K, are recombination

coefficients of the injection and the back surfaces, respectively. In the DR regime,

(2) where JG is the permeation flux density in the presence of gas alone, and D, is the bulk diffusion coefficient in the injection side. In the RD regime, if J, s 4

P,

(3) where D, is the bulk diffusion coefficient in the back side. In the DD regime, J,+

D,RP

D,x,, “’

It is seen from eqs. (l)-(4) that each transport regime is characterized by a specific parameter dependence of J,. It means that we can distinguish the transport regime by the parameter dependence of J,. It is also seen from eq. (3) that we can evaluate K, with J, and J, in the RD regime. In the actual calculation, however, we numerically solve eqs. (3)-(5) in ref. [5] instead of eq. (3) to avoid errors caused by the approximation. 2.2. Semi theoretical estimation of the recombination coefficient 2.2.1. Relation between the recombination coefficient and the adsorption probability The flux density of the recombinative

desorption

(RI from metals is often assumed to be given by R=KC’,

(5)

where K is the rate constant called the (surface) recombination coefficient and C is the bulk hydrogen concentration just beneath the surface. (We have also assumed eq. (51 in deriving eqs. (l)-(4).) When hydrogen gas and hydrogen dissolved in a metal are in equilibrium, the recombination coefficient can be related to the adsorption probability and the solubility as follows. The adsorption (uptake) flux density of hydrogen gas to metal is generally given by &,ps(O), where lo is the flux density of hydrogen molecules on metal surface per unit pressure, p the pressure, and s(0) the adsorption probability at surface coverage of 13. In equilibrium, the adsorption flux density must be equal

to the desorption (release) flux density (RI. In addition, the hydrogen concentration in metal obeys Sieverts’ law, i.e., C = C,p’/’ with C,, Sieverts’ constant. Thus the following relation holds in equilibrium: R s=

50 ps(O) ( C,,P’q2

=-

l,s(O) C,:

When 0 (rc 1, s(0) and hence R/C2 are practically independent of 0 or C so that recombination coefficient K can be defined as R/C=. We think that this provides the basis of eq. (5). Since the desorption flux density must be a function of 0, eq. (6) seems valid even for steady-state release as long as quasi-equilibrium holds between t9 and C. When we apply eq. (6) to the steady-state release, we implicitly assume this quasi-equilibrium; in other words, we assume that the hydrogen exchange between the surface adsorption sites and the bulk solution sites is much faster than the recombinative desorption. It should be emphasized that eq. (6) itself holds irrespective of the detailed mechanism of the uptake and the release because we have not assumed any detailed mechanism in the above discussion. (Indeed the functional form of s(0) and whether the quasi-equilibrium holds or not should depend on the detailed mechanism). Waelbroeck et al. [7,8], Pick and Sonnenberg (referred to as PS) [9], and Richards [lO,ll] have already obtained similar expressions for K, but their derivation is different from ours in that they first assumed the elementary processes involved in the uptake and the release, and then considered the balance between them. Such derivation seems to make the generality of eq. (6) unclear. In eq. (61, l,, is given by the kinetic theory of gases and C,, has been measured for many metals and alloys. If s(0) is known as well, we can estimate K semitheoretically using eq. (6). In other words, the ratio of the measured K to [0/Ci (the R/C2 calculated with s(0) = 1) gives an estimate of the adsorption probability. These are important conclusions for the discussion in sections 4.3 and 4.4. (Although it has been assumed [9,10] that s(O) is close to unity for clean surface of transition metals, recent experiments [12] have revealed that it is not necessarily the case. We should not simply assign unity to s(O). See also the following section.) 2.2.2. Expression for the adsorption probability It is the interaction between hydrogen and a metal in the vicinity of the metal surface that defines the adsorption probability. In fact there have been some

T. Nagasakiet al. / Permeationand surface recombinationcoeficient of D for Fe

GAS

231

the activation barrier or the potential-energy encountered in each process;

BULK

maximum

s*(O) = $’ exp( - 2 E,/R,T),

(9)

(8)

EC + max( E,,

E, - Es)

RGT

2 m=(E,, &-Es) R,T

Fig. 2

One-dimensional potential energy diagram for hydrogen near metal surfaces.

attempts to determine the potential-energy surface (PES) of metals for hydrogen theoretically. However, instead of the strict treatment, one-dimensional potential-energy diagram is often used to describe the interaction of hydrogen with a metal surface. It is shown in fig. 2 for endothermic occluders. Although in general the PES is not one-dimensional [13,14], it could be used to roughly see how, and to what extent, the activation barrier for adsorption affects the recombination coefficient as well as the adsorption probability. According to Richards [lO,ll], the adsorption probability s(e) may be expressed as

SC@> =s*(@)+ de) + so(e) =sz(O)(l

-e)*+.si(o)(l

-e> +s,,

(7)

where s,(e), s,(e), and s,,(e) are adsorption probabilities by different mechanisms. (The bulk concentration is assumed to be far below saturation.) The sz process is the ordinary dissociative adsorption, and only this process was considered in the PS treatment [9]. In the si process, an incident molecule disassociates, and, of the two disassociated atoms, one is adsorbed in the surface adsorption sites and the Other goes directly into the bulk solution sites without being thermalized in the adsorption sites. In the so process, an incident molecule disassociates, and the two disassociated atoms go directly into the bulk solution sites. The latter two processes were postulated by Richards [lO,ll] as alternative uptake processes which may be important when the adsorption sites are saturated. (In the present papers we include these processes in adsorption and the corresponding reverse processes in desorption.) On the basis of the potential energy diagram shown in fig. 2, Richards expressed s2(0), s,(O), and s,(O) in terms of

I’

WV

where R, is the gas constant and T the temperature. The exponential terms in eqs. (8)-(10) express the fraction of the impinging molecules with “normal energy” higher than the barrier, or the fraction of the impinging molecules which can surmount the one-dimensional energy barrier along the surface with their translational energy alone. (The prefactors have some ambiguity and it was assumed that ~0”= sf/2 = si = l/4 in numerical calculation in the present paper.) On the other hand, in equilibrium, 0 can be related to c (the occupancy of the bulk solution sites, i.e., C = NC with N the number of solution sites per unit volume) by statistical thermodynamics [lo]; &=cexp[(G,-G;)/R,T]-AC,

(11)

where G, is the free energy of the bulk solution sites, and Gs that of the surface adsorption sites. In the often-assumed cases where entropy effect and diffusion effect are negligible, Gs and Gs can be replaced by -Es and - Ei, respectively. Using eq. (ll), Richards [lo] obtained so exp( - E,/R,T) s(e)

=

~.Q(o)(I

-eji=

i=O

i i=O

(1 +hc)’

’

(12) where Ei is the activation barrier encountered in the si process, explicitly written in eqs. (8)-(10). Substituting eq. (12) into eq. (6) we have a semitheoretical estimate of R/C2 as a function of the activation barriers.

3. Experiment 3.1. Experimental method The experimental apparatus was the same as in the experiment for copper [3] and silver [4]. It consists of an ion accelerator for deuterium implantation and a permeation setup installed in its target chamber. Details have been described elsewhere [l-3]. As a sample

232

T. Nagasaki et al. / Permeation and surface recombination coefficient of D for Fe

we used polycrystalline iron foil (99.99 + % purity, Goodfellow Metals Ltd.). It was mechanically polished, cut into a disc (19 mm in diameter and 0.14 mm in thickness), and then welded to a sample holder made of nickel. We repeatedly cleaned the back surface of the sample in situ by argon ion bombardment (3 keV, < 1 WA) throughout the experiment. (Part of the inner surface of the holder was covered by iron foil to prevent nickel atoms from being sputtered from the holder and implanted into the sample.) For the injection surface, the deuterium implantation itself was used as cleaning procedure. We did not analyze the surface, however. The implanted ions were 5 keV D.:. In the measurement of the temperature dependence of the permeation flux, we fixed the implantation flux density at 1.0 X 10” D-atoms cmm2 s- ‘. The permeation flux was measured with a quadrupole mass spectrometer (QMS) which was calibrated against a standard D, flow [l] in the end of the measurement each day. 3.2. Experimental

t / min Fig. 3. An example of the observed permeation spike. The spike appeared in the second implantation (t 2 28 min) as well as in the first one (0 5 t 5 22 min) in spite of the short interval between them. The implantation flux density was 1.0X 1Ol5 D-atoms cm-’ s-‘.

results

Even in the absence of the deuterium implantation, there was appreciable deuterium in the form of HD and D, (the QMS signals for m/z = 3 and 4) in the back chamber (the vacuum chamber facing the back surface of the sample). We refer to the flux of this background deuterium as U,. It seemed that whereas it was mainly due to the release from the vacuum components at low temperature, it included considerable gas-driven permeation of deuterium through the sample and the sample holder as well at high temperature. We accordingly define Uo as the deuterium flux in the form of HD or D, resulting from the gas-driven permeation through the sample. However, we could not separate Uo from U,. The deuterium implantation caused deuterium permeation, and increased the flux of HD and D, in the back chamber. We corresponding define U, as the increment in the deuterium flux in the form of HD or D, due to the deuterium implantation. In the present paper we express the above deuterium fluxes in terms of the number of deuterium atoms per implantation area (0.79 cm2). Since the increase in HDO and D,O due to the implantation was small, U, and U, approximate the flux densities of deuterium permeation, J, and JG, respectively. The time dependence of U, was not simple. We often observed the permeation spike, i.e., the initial maximum in U, especially in the range of 300-500°C. Although U, usually became constant within _ 1 h,

the permeation spike often appeared again in the subsequent implantation even when the interval between the implantation was short, say, 10 min. An example of such behavior is shown in fig. 3. It contrasts with the results for nickel, where once the permeation flux leveled off, the permeation spike often disappeared in the following implantation after 1 h interval (see fig. 3 and table 3 of ref. [l]). In the present paper, however, we focus on lJp( + Jp) in a steady state. Below 85O”C, we got reproducible results for U, in a steady state by bombarding the back surface of the sample with argon ions in the beginning of the measurement each day. Fig. 4 shows the temperature dependence of the U, together with that of U, below 850°C. Whereas U, increases with temperature above _ 200°C it is roughly constant below u 150°C. When the sample was heated above 900°C however, the prebombardment was not effective enough. The U, measured during temperature increase did not agree well with the U, measured during temperature decrease. Besides, U, tended to change day by day. We thus measured U, while bombarding the back surface with argon ions continuously. In this case the results were reproducible. They are shown in fig. 5 as a function of reciprocal temperature; the U, in fig. 4 is also shown for comparison. In the temperature range where both set of data exist, they agree well. Note that the value and the gradient of U, changes abruptly around 920°C.

T. Nagasaki et al. / Permeation and surface recombination coefficient of D for Fe

sponds to the R,/x, in the present experiment [16]. Since D,/D, is unlikely to be far from unity, the correspondence may suggest that the transport regime in the sample is DD below _ 150°C (see eq. (4)). On the other hand, the values of n at 600 and 800°C are most consistent with the equation for the RD regime (see eq. (3)). Moreover, we observed such temperature dependence for nickel [l], copper [3], and silver [4] as well as iron, and believe that the mechanism responsible for it is common in these metals. In the experiment for nickel, we measured the dependence of UP on 4r, Uo, and E (incident deuterium energy) as well as on T (temperature). Comparing the results with eqs. (l)-(4), we found that the deuterium transport in the nickel sample was controlled by the RD regime above the transition temperature and by the DD regime below it. We thus conclude that for a-iron, the transport regime is RD above N 200°C and DD below _ 150°C.

T (IOO'C) 106765

4

3

1

2

233

5 keV OS' ir Fe

000

T (IOO'C)

0.5

1.0

1.5

2.0

2.5

3.0

1110

3.5

IO'K / T Fig. 4. Temperature dependence of UP and Ua in a steady state below 850°C. The back surface of the sample was bombarded with argon ions in the beginning of the measurement each day. The implantation flux density was 1.0~ 1015D-atoms cm-’ SK’.

9

6

7

6

14C 5 keV Da'

i

-* Fe

m

Y We also tried to measure the dependence of UP on the implantation flux density &~r. Although we obtained n( = alogll,/~log~,) = 0.63 at 800°C and n = 0.57 at 600°C they are somewhat unreliable because of the scatter of the data.

s

4. Discussion 4. I Identification

of the transport

6 i

regime

As mentioned in section 3.2, UP changed in its value and gradient around 920°C (fig. 5). This temperature is close to the phase transformation temperature of iron (+ 911°C [15]>, indicating that the change is due to the phase transformation. For a-iron, which is the phase below the transformation temperature, U, increase with temperature above - 200°C whereas U, is roughly constant below _ 150°C. The value of lJ,/+,, below N 150°C is about 10-4, which roughly corre-

0

12 1 a.7

0

0.6

Ar simul.-bombarded Ar pre-bombarded 0.9 lo8K/

1.0

1.1

1.2

T

Fig. 5. Temperature dependence of UP and Ua in a steady state above 600°C. The diamonds represent the data measured while the back surface of the sample was bombarded with argon ions simultaneously. The circles are the same data as shown in fig. 4. The implantation flux density was 1.0x 1015 D-atoms cm-Zs-l.

234

T. Nagasakiet al. / Permeationand surface recombinationcoefficientofD for Fe T (IOO’C)

For y-iron, which is the phase above the transformation temperature, the DR and the DD regimes can be ruled out because UP increases with increasing temperature, and is much larger than U, in the DD regime. On the other hand, the behavior of Ua - Ua decreases in its value and increases in its gradient with the transformation from the a-phase to the y-phase agrees qualitatively with that of the diffusion coefficient [17]. Thus, although the RR regime is also possible, the RD regime is probably the case with y-iron. We will analyze the data assuming the RD regime for -y-iron in the following.

96766

3

4

-12 -

-13

4.2. Evaluation of the recombination coefficient from the permeation flux density As explained in section 2.1., we can evaluate the recombination coefficient K, with the permeation flux densities J, and Jo in the RD regime. However, while U, is comparable to or even larger than Up at high temperature as seen from figs. 4 and 5, we could not separate U, from U, in the measurement. We hence estimated U, at the phase transformation temperature from the change in U, there. According to ref. [17], Jo (U,) in y-iron is 30% of Jo (U,> in a-iron at the transformation temperature. On the other hand, U, in y-iron is 80% of U, in a-iron at the transformation temperature. This difference suggests that UG/UB = 0.3 in a-iron and that UG/UB = 0.1 in y-iron at the temperature. Indeed the ratio of U,/U, will deviate from these values as temperature increases or decreases. However, in the temperature range far below the transformation temperature, U, itself is much smaller than U, so that the values of UG/UB does not affect the evaluation of K, considerably. Thus we assume that Jo = U, = 0.3U, for a-iron and that Jo = U, = O.lU, for y-iron in the actual calculation of K,. As the diffusion coefficient necessary for the evaluation of K,, we have chosen the data in ref. [17] because they cover both (Yand y-phases as well as they are close to the recommended value [18] for a-iron. It should be noted that the literature data for the diffusion coefficient of hydrogen (deuterium) in a-iron have scattered widely [l&19], leading to some uncertainty in the evaluated K,. As for the parameter y( = (K,/K,)‘/2), which is also necessary for the evaluation of K,, we assumed y to be unity. In the actual experiment it may not have been the case because the cleanness of the back surface could be different from that of the injection surface. Nevertheless, the assumption seems valid because the value of y affects K, only a little as long as the transport is basically controlled by the RD regime.

-16 0.6

1.0

1.2

1.4 iOaK/

1.6

1.6

2.0

T

Fig. 6. Temperature dependence of K, for a-iron evaluated with the CJ, shown in fig. 4.

Fig. 6 shows the temperature dependence of the K, for a-iron in the range of 300-850°C calculated with the U, in fig. 4. It is well described by either K, =a,T-‘/2

exp(Q,/R,T),

(13)

or Ki = a2

ew(QJRJ),

(14)

where a,, a2, Q, and Q2 are listed in table 1. Although the T-l/* dependence of the recombination coefficient may be expected from that of la (see eq. (6)), eq. (14) gives practically the same result as eq. (13). Fig. 7 shows the temperature dependence of the K, around the transformation temperature calculated with the U, in fig. 5. The K, for y-iron is well described by eq. (13) or (14) with the parameters listed in table 1. The discussion in this section is based on the assumption that the transport regime is RD for y-iron. If it is wrong, the K, and the U, calculated for -y-iron are incorrect. Though the U, for a-iron is also erroneous, the K, for a-iron is hardly affected. Unfortunately, we do not know what surface state composition and structure - the K, evaluated above

235

T. Nagasakiet al. / Penneation and surface recombinationcoefficientof D for Fe

T (1OO'C) 1110

9

6

7

6

defects produced in the present experiment might have similar nature and hence increase K,.

-14

4.3. Semitheoretical estimation of the recombination coI phase

efficient

a phase

8’

Fig. 8 shows the semitheoretical estimates of the recombination coefficient based on eq. (6). A broken line in the figure indicates &/C~ for o-iron. This value multiplied by the adsorption probability yields the recombination coefficient, or strictly speaking, the R/C*. Solid circles are the R/C* calculated with the s(f9 < 1) of H, gas at 300 K reported by Berger and Rendulic [12] (1.2 X lo-*, 1.5 X 10m3, and 1.6 X lo-* for clean Fe(llO), (100) and (111) surfaces, respectively). The dash-dotted lines represent the R/C* calculated with eq. (12) for a release flux density of 1.0 X 1015 D-atoms

Ooo

i

03

00°

-15

P

'E

L‘ 5 -16 r(

-P

T (1OO'C)

0 Ar simul.-bombarded 0 Ar pre-bombarded

105765

I

-17' 0.7

0.6

0.9 ldK/

1.0

1.1

,,,I,

T

a, (cm4 s-l K-‘/‘) Q, &J mol-‘) aa (cm4 s-t) Q, &J mol-‘)

a-iron

y-iron

5.t35x10-‘6 36.0 1.26x10-” 39.3

5.85 x lo- l8 73.5 9.93x 10-m 78.8

1

2

r&o’ / /’ /i-

al

-12

\

-14

S

-16

N

0" I-!

\

/

/ /NH I)-

/

,‘/’

5ergtr

1

-16

I

0.5

of the measured K,

I

-10 -

i

dependence

3

I

-6 -

Fig. 7. Temperature dependence of K, for iron around the transformation temperature evaluated with U, shown in fig. 5.

Table 1 Parameters in eqs. (8) and (9) describing the temperature

4

r

1.2

corresponds to. The fact that the permeation spike recovered easily implies that there was a kind of source supplying impurities continuously onto the injection surface of the sample. Although the impurities should have been sputtered away by the deuterium implantation, it could not be ruled out that the appreciable amount of the impurities remained on the surface to reduce K, even during the deuterium implantation. We also notice that the deuterium implantation will produce defects on the injection surface. Rendulic et al. 1201found that the defects on Ni(ll1) surface introduced sites for nonactivated hydrogen adsorption. The

I

1.0

1.5

2.0

2.5

3.0

I 3.5

1O'K / T Fig. 8. Temperature dependence of the semitheoretically estimated recombination coefficient for a-iron. The broken line represents &/Ci. The solid circles represent the R/C2 calculated with ~(0 g 1) measured by Berger and Rendulic 1121.The dash-dotted lines represent the R/C’ calculated with Ec as a parameter; the release flux density was fixed at 1.0~10’s D-atoms cme2 s-l , i.e., the actual release flux density in the present experiments.

T. Nagasakiet al. / Permeationand surface recombinationcoefficientof D for Fe

236

T (IOO'C)

1067654

3

0 K, (this

-6

1

2

work)

0 Wampler q

Andrew

/

/

/

/

/

/

/

/

/

0

7 In

-5 \ L

-12

-14

-0” -16

-16 i 0.5

1.0

1.5

2.0

2.5

3.0

fig. 9. Some literature data of the recombination coefficient K are also shown for comparison. Wampler [22,23] evaluated K from the release rate of the deuterium in a polycrystalline iron foil. While he found 0.1 monolayer each of oxygen and carbon on the surface, he estimated the reduction in K due to the oxygen to be about 20%. Andrew and Haasz 1241 evaluated K from the permeation flux through a polycrystalline iron membrane driven by molecular and atomic hydrogen; surface composition was 90% Fe, 4% 0, 6% C, < 1% S, and < 1% others. It is noteworthy that the K,, when extrapolated to lower temperature, agrees with Wampler’s data. The temperature range where we evaluated K, are situated far above the transition temperature of the R/C2, indicating that 0 was much smaller than unity there. Thus the ratio of the K, to &/C’i suggests that s(O) = 10-2-10-’ at 300-850°C. This value seems to be consistent with the adsorption probability measured by Berger and Rendulic [12] using a molecular beam. Moreover, if K, is extrapolated to room temperature, it is comparable to the semitheoretical estimates using

3.5 T (IOO’C)

103K / T 1110

Fig. 9. Comparison of K, and R/C* determined for a-iron. Some literature data for the recombination coefficients (Wampler [22,23], Andrew and Haasz [24]) are also shown.

cm-* s-l (the actual release flux density) with E, as a parameter. The values of C, and Ek were taken from refs. [17] and [21], respectively; E, was assumed to be equal to E,, which was taken from ref. [18]. As seen from the figure, the R/C2 for the fixed release flux density changes abruptly around a temperature. This transition is caused by the saturation of the surface adsorption sites. Above the transition temperature, 0 < 1 so that the s2 process (“ordinary” adsorption) is dominant; below the transition temperature, 13i 1 so that the s0 process is dominant. In both cases, the recombination coefficient can be defined as R/C2 because R is practically proportional to C2. Near the transition temperature, however, R is a complex function of C, so that the recombination coefficient cannot be defined. 4.4 Comparison between the experimentally and semithe-

9

7

6

-14

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g

F4

-16

,/*

/’ 0 Ar simul.-bombarded 0 Ar pre-bombarded

-17'

0.7

0.6

0.9 IdK/

oretically determined recombination coefficients

The K, and the R/C2 determined for a-iron in the previous sections (figs. 6 and 8) are shown together in

6

Fig. 10. Comparison mation temperature.

1.0

1.1

l., 3

T

of K, and R/C2 around The symbols correspond fig. 5.

the transforto those in

T. Nagasakiet al. / Permeationand surface recombinationcoefficientof D for Fe

their data for ~(0 s 1). We can say that K, evaluated in the present work agrees rather quantitatively with the semitheoretical estimate using eq. (6). Although impurities and defects might have affected K, as pointed out in section 4.2, there is no need to postulate their effects in accounting for the present results. This quantitative agreement seems to demonstrate that the release kinetics reflects the activation barrier for adsorption.

Fig. 10 shows K, and R/C2 around the transformation temperature. As far as we know, there are no literature data for the adsorption probability of hydrogen (deuterium) on y-iron. The ratio of the K, to the R/C2 with E, = 0 (s(0) = l/4) for the y-phase suggests that s(0) = 0.1 around 1000°C. There may be a small activation barrier for hydrogen adsorption on y-iron.

5. Summary We implanted deuterium ions (5 keV D:, 1.0 X 1015 D-atoms cmm2 SK*) into an iron membrane (99.99 + % purity, 0.14 mm thickness) and measured the permeation flux in the range of 30-1050°C. The temperature dependence of the permeation flw changed abruptly around 920°C because of the phase transformation, In addition the temperature dependence for the a-phase changed around 150-200°C; the permeation flux increased with increasing temperature above 2OO”C, whereas it was roughly constant below 150°C. This temperature dependence is essentially the same as that observed for nickel, copper, and silver, and suggests that the transport regime for a-iron is RD above 200°C and DD below 150°C. From the permeation flux density in the RD regime, we evaluated the recombination coefficient of deuterium on iron surface. On the other hand, we estimated the recombination coefficient for u-iron semitheoretically using the literature data of the adsorption probability and the solubility. The estimation is based on consideration of the equilibrium condition, thus being valid irrespective of the detailed mechanism of the hydrogen uptake into and release from the metal. The value evaluated with the permeation flux density agreed well with the semitheoretical estimate. This agreement further indicates that the release kinetics reflects the activation barrier for the hydrogen (deuterium) adsorption.

231

Appendix. Definition of the flux densities The definition of the flux densities in ref. [l] seems somewhat ambiguous. Let us consider +o as an example. In ref. [l], we defined I& as the flux density of hydrogen atoms which migrate from the subsurface (bulk) solution sites to the surface adsorption sites, recombine there and are desorbed as molecules. While this definition appears to include two serial processes of the migration to the surface and the recombinative desorption, the flux densities of the two processes can be different; hydrogen atoms which migrate from the subsurface (bulk) solution- sites to the surface adsorption sites may migrate back to the solution sites before recombining with other hydrogen atoms on the surface. In particular, when quasi-equilibrium holds between hydrogen in the adsorption sites and that in the solution sites, the bulk-to-surface flux is practically equal to the surface-to-bulk flux, being much larger than the desorption flux. As shown in section 2.2, the flux density which can be related to the bulk concentration via the recombination coefficient is none other than the flux density of the recombinative desorption or the dissociative adsorption. We accordingly define JG and J, simply as desorption flux density in the present paper. (The flux densities +o, +o, and JIP [1,3,4] should be defined similarly.) Nevertheless the equations in ref. [l] are unaffected by this change in the definition.

References 111 T. Nagasaki, R. Yamada, M. Saidoh and H. Katsuta, J. Nucl. Mater. 151 (1988) 189. M T. Nagasaki, R. Yamada and H. Ohno, J. Nucl. Mater. 179-181 (1991) 335. [31 T. Nagasaki, R. Yamada and H. Ohno, J. Vat. Sci. Technol. A10 (1992) 170. [41 T. Nagasaki, R. Yamada and H. Ohno, J. Nucl. Mater. 195 (1992) 324. 151 T. Nagasaki, R. Yamada and H. Ohno, J. Nucl. Mater. 191-194 (1992) 258. I61 T. Nagasaki and H. Ohno, J. Vat. Sci. Technol. A, in press. 171 F. Waelbroeck, Jiil-1966 (1984). 181 I. Ali-Khan, K.J. Dietz, F.G. Waelbroeck and P. Wienhold, J. Nucl. Mater. 76&77 (1978) 337. [91 M.A. Pick and K. Sonnenberg, J. Nucl. Mater. 131 (1985) 208. [lOI P.M. Richards, J. Nucl. Mater. 152 (1988) 246. 1111 S.M. Myers, P.M. Richards, W.R. Wampler and F. Besenbacher, J. Nucl. Mater. 165 (1989) 9.

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[12] H.F. Berger and K.D. Rendulic, Surf. Sci. 2.51/2.52 (1991) 882. [13] G. Anger, A. Winkler and K.D. Rendulic, Surf. Sci. 220 (1989) 1. [14] J. Harris, Surf. Sci. 221 (1989) 335. [15] JANAF Thermochemical Tables, 2nd. ed., NSRD-NBS37 (1971). [16] H.H. Anderson and J.F. Ziegler, Hydrogen Stopping Powers and Ranges in All Elements, vol. 3 of The Stopping and Ranges of Ions in Matter, ed. J.F. Ziegler (Pergamon, New York, 1977). [17] Th. Heumann and D. Primas, Z. Naturforsch. 21a (1966) 260.

[18] J. Volkl and G. Alefeld, in Hydrogen in Metals I, eds. G. Alefeld and J. Vdlkl (Springer, Berlin, 1978), p. 321. [19] K. Kiuchi and R.B. McLellan, Acta Metall. 31 (1983) 961. [20] K.D. Rendulic, A. Winkler and H.P. Steinriick, Surf. Sci. 185 (1987) 469. [21] F. Bozso, G. Ertl, M. Grunze and M. Weiss, Appl. Surf. Sci. 1 (1977) 103. [22] W.R. Wampler, Appl. Phys. Lett. 48 (1986) 405. [23] W.R. Wampler, J. Nucl. Mater. 145-147 (1987) 313. [24] P.L. Andrew and A.A. Haasz, J. Vat. Sci. Technol. A8 (1990) 1807.